if 3^x=9^y then find the value of x:y
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Step-by-step explanation:
3x+y=9⟹y(3x+y)=y(9)⟹3xy+y2=9y
⟹3xy=9y−y2⟹xy=3y−13y2
In order to find the maximum value of x y we differentiate 3y−13y2
ddy(3y−13y2)=3−23y
For maximum value
3−23y=0⟹23y=3⟹y=92
∴(xy)max=3(92)−(13)×(92)2
=(272)−(274)
=(274)=6.75
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